+unify :: TvSubstEnv -- An existing substitution to extend
+ -> Type -> Type -- Types to be unified
+ -> UM TvSubstEnv -- Just the extended substitution,
+ -- Nothing if unification failed
+-- We do not require the incoming substitution to be idempotent,
+-- nor guarantee that the outgoing one is. That's fixed up by
+-- the wrappers.
+
+-- Respects newtypes, PredTypes
+
+unify subst ty1 ty2 = -- pprTrace "unify" (ppr subst <+> pprParendType ty1 <+> pprParendType ty2) $
+ unify_ subst ty1 ty2
+
+-- in unify_, any NewTcApps/Preds should be taken at face value
+unify_ subst (TyVarTy tv1) ty2 = uVar False subst tv1 ty2
+unify_ subst ty1 (TyVarTy tv2) = uVar True subst tv2 ty1
+
+unify_ subst (NoteTy _ ty1) ty2 = unify subst ty1 ty2
+unify_ subst ty1 (NoteTy _ ty2) = unify subst ty1 ty2
+
+unify_ subst (PredTy p1) (PredTy p2) = unify_pred subst p1 p2
+
+unify_ subst t1@(TyConApp tyc1 tys1) t2@(TyConApp tyc2 tys2)
+ | tyc1 == tyc2 = unify_tys subst tys1 tys2
+
+unify_ subst (FunTy ty1a ty1b) (FunTy ty2a ty2b)
+ = do { subst' <- unify subst ty1a ty2a
+ ; unify subst' ty1b ty2b }
+
+ -- Applications need a bit of care!
+ -- They can match FunTy and TyConApp, so use splitAppTy_maybe
+ -- NB: we've already dealt with type variables and Notes,
+ -- so if one type is an App the other one jolly well better be too
+unify_ subst (AppTy ty1a ty1b) ty2
+ | Just (ty2a, ty2b) <- repSplitAppTy_maybe ty2
+ = do { subst' <- unify subst ty1a ty2a
+ ; unify subst' ty1b ty2b }
+
+unify_ subst ty1 (AppTy ty2a ty2b)
+ | Just (ty1a, ty1b) <- repSplitAppTy_maybe ty1
+ = do { subst' <- unify subst ty1a ty2a
+ ; unify subst' ty1b ty2b }
+
+unify_ subst ty1 ty2 = failWith (misMatch ty1 ty2)
+
+------------------------------
+unify_pred subst (ClassP c1 tys1) (ClassP c2 tys2)
+ | c1 == c2 = unify_tys subst tys1 tys2
+unify_pred subst (IParam n1 t1) (IParam n2 t2)
+ | n1 == n2 = unify subst t1 t2
+unify_pred subst p1 p2 = failWith (misMatch (PredTy p1) (PredTy p2))
+
+------------------------------
+unify_tys = unifyList unify
+
+unifyList :: Outputable a
+ => (TvSubstEnv -> a -> a -> UM TvSubstEnv)
+ -> TvSubstEnv -> [a] -> [a] -> UM TvSubstEnv
+unifyList unifier subst orig_xs orig_ys
+ = go subst orig_xs orig_ys
+ where
+ go subst [] [] = return subst
+ go subst (x:xs) (y:ys) = do { subst' <- unifier subst x y
+ ; go subst' xs ys }
+ go subst _ _ = failWith (lengthMisMatch orig_xs orig_ys)
+
+------------------------------
+uVar :: Bool -- Swapped
+ -> TvSubstEnv -- An existing substitution to extend
+ -> TyVar -- Type variable to be unified
+ -> Type -- with this type
+ -> UM TvSubstEnv
+
+uVar swap subst tv1 ty
+ = -- check to see whether tv1 is refined
+ case (lookupVarEnv subst tv1) of
+ -- yes, call back into unify'
+ Just ty' | swap -> unify subst ty ty'
+ | otherwise -> unify subst ty' ty
+ -- No, continue
+ Nothing -> uUnrefined subst tv1 ty
+
+
+uUnrefined :: TvSubstEnv -- An existing substitution to extend
+ -> TyVar -- Type variable to be unified
+ -> Type -- with this type
+ -> UM TvSubstEnv
+
+-- We know that tv1 isn't refined
+uUnrefined subst tv1 ty2@(TyVarTy tv2)
+ | tv1 == tv2 -- Same, do nothing
+ = return subst
+
+ -- Check to see whether tv2 is refined
+ | Just ty' <- lookupVarEnv subst tv2
+ = uUnrefined subst tv1 ty'
+
+ -- So both are unrefined; next, see if the kinds force the direction
+ | k1 == k2 -- Can update either; so check the bind-flags
+ = do { b1 <- tvBindFlag tv1
+ ; b2 <- tvBindFlag tv2
+ ; case (b1,b2) of
+ (DontBindMe, DontBindMe) -> failWith (misMatch ty1 ty2)
+ (DontBindMe, _) -> bindTv subst tv2 ty1
+ (BindMe, _) -> bindTv subst tv1 ty2
+ (AvoidMe, BindMe) -> bindTv subst tv2 ty1
+ (AvoidMe, _) -> bindTv subst tv1 ty2
+ }
+
+ | k1 `isSubKind` k2 -- Must update tv2
+ = do { b2 <- tvBindFlag tv2
+ ; case b2 of
+ DontBindMe -> failWith (misMatch ty1 ty2)
+ other -> bindTv subst tv2 ty1
+ }
+
+ | k2 `isSubKind` k1 -- Must update tv1
+ = do { b1 <- tvBindFlag tv1
+ ; case b1 of
+ DontBindMe -> failWith (misMatch ty1 ty2)
+ other -> bindTv subst tv1 ty2
+ }
+
+ | otherwise = failWith (kindMisMatch tv1 ty2)
+ where
+ ty1 = TyVarTy tv1
+ k1 = tyVarKind tv1
+ k2 = tyVarKind tv2
+
+uUnrefined subst tv1 ty2 -- ty2 is not a type variable
+ -- Do occurs check...
+ | tv1 `elemVarSet` substTvSet subst (tyVarsOfType ty2)
+ = failWith (occursCheck tv1 ty2)
+ -- And a kind check...
+ | k2 `isSubKind` k1
+ = do { b1 <- tvBindFlag tv1
+ ; case b1 of -- And check that tv1 is bindable
+ DontBindMe -> failWith (misMatch ty1 ty2)
+ other -> bindTv subst tv1 ty2
+ }
+ | otherwise
+ = pprTrace "kind" (ppr tv1 <+> ppr k1 $$ ppr ty2 <+> ppr k2) $
+ failWith (kindMisMatch tv1 ty2)
+ where
+ ty1 = TyVarTy tv1
+ k1 = tyVarKind tv1
+ k2 = typeKind ty2
+
+substTvSet :: TvSubstEnv -> TyVarSet -> TyVarSet
+-- Apply the non-idempotent substitution to a set of type variables,
+-- remembering that the substitution isn't necessarily idempotent
+substTvSet subst tvs
+ = foldVarSet (unionVarSet . get) emptyVarSet tvs
+ where
+ get tv = case lookupVarEnv subst tv of
+ Nothing -> unitVarSet tv
+ Just ty -> substTvSet subst (tyVarsOfType ty)
+
+bindTv subst tv ty = return (extendVarEnv subst tv ty)